MicroStructPy: A statistical microstructure mesh generator in Python
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Kenneth A. Hart↗
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Multiscale Modeling of Grain Boundaries in ZrB2: Structure, Energetics, and Thermal Resistance
A combination of ab initio, atomistic and finite element methods (FEM) were used to investigate the structures, energetics and lattice thermal conductance of grain boundaries for the ultra high temperature ceramic ZrB2. Atomic models of idealized boundaries were relaxed using density functional theory. Information about bonding across the interfaces was determined from the electron localization function. The Kapitza conductance of larger scale versions of the boundary models were computed using non-equilibrium molecular dynamics. The interfacial thermal parameters together with single crystal thermal conductivities were used as parameters in microstructural computations. FEM meshes were constructed on top of microstructural images. From these computations, the effective thermal conductivity of the polycrystalline structure was determined.
Lawson, John W.↗
Recent Developments to the Porous Microstructure Analysis (PuMA) Software
Introduction The Porous Microstructure Analysis (PuMA) software is an open source framework for image-based simulation, primarily used to determine effective properties based on material microstructure. PuMA was originally developed for the study of NASA thermal protection materials; however, many of the solvers in PuMA have applicability to a broad range of materials science applications. PuMA version 3.2 computes material surface area, pore diameters, effective thermal conductivity, continuum and rarefied tortuosity, and permeability. For anisotropic materials, PuMA can estimate material orientation and compute anisotropic thermal conductivity and elasticity. In this talk, a brief overview of the PuMA software and underlying methods will be presented, as well as some recent and ongoing developments, including the use of immersed boundary methods for image-based simulation and the development of a new weave segmentation tool, called TomoSAM. Cut-Cell method for heat and mass transfer For simulations on complex microstructures, traditional unstructured meshing techniques often prove to be difficult and time-intensive. Voxel-based solvers, which represent the surface as a staircase structure, are relatively simple to implement but can lose accuracy when feature resolution is poor. In this work, we present a novel 3D cut-cell method for solving the variable coefficient Poisson equation on complex microstructures, suitable for the determination of effective thermal conductivity or tortuosity of a material. The method uses a Marching Cubes/Marching Squares surface reconstruction to create cut-cells and determine geometric quantities. A flux-correction method is extended to 3D, with least squares gradient reconstruction, to solve for the boundary fluxes in the cut-cells. Verification cases show the solver achieves globally 2nd order accuracy on complex microstructures. TomoSAM TomoSAM, a module of the PuMA software, has been developed as a plugin for 3D Slicer, a software platform used for 3D image processing and visualization. It utilizes the Segment Anything Model (SAM), a deep learning model capable of identifying objects and generating image masks based on minimal user input. This feature enables efficient segmentation of complex 3D datasets, particularly of woven materials, from tomography or similar imaging methods, reducing the need for manual segmentation.
Tomography↗
Recent Developments to the Porous Microstructure Analysis (PuMA) Software
The Porous Microstructure Analysis (PuMA) software is an open source framework for image-based simulation, primarily used to determine effective properties based on material microstructure. PuMA was originally developed for the study of NASA thermal protection materials; however, many of the solvers in PuMA have applicability to a broad range of materials science applications. PuMA version 3.2 computes material surface area, pore diameters, effective thermal conductivity, continuum and rarefied tortuosity, and permeability. For anisotropic materials, PuMA can estimate material orientation and compute anisotropic thermal conductivity and elasticity. In this talk, a brief overview of the PuMA software and underlying methods will be presented, as well as some recent and ongoing developments, including the use of immersed boundary methods for image-based simulation and the development of a new weave segmentation tool, called TomoSAM. Cut-Cell method for heat and mass transfer For simulations on complex microstructures, traditional unstructured meshing techniques often prove to be difficult and time-intensive. Voxel-based solvers, which represent the surface as a staircase structure, are relatively simple to implement but can lose accuracy when feature resolution is poor. In this work, we present a novel 3D cut-cell method for solving the variable coefficient Poisson equation on complex microstructures, suitable for the determination of effective thermal conductivity or tortuosity of a material. The method uses a Marching Cubes/Marching Squares surface reconstruction to create cut-cells and determine geometric quantities. A flux-correction method is extended to 3D, with least squares gradient reconstruction, to solve for the boundary fluxes in the cut-cells. Verification cases show the solver achieves globally 2nd order accuracy on complex microstructures. TomoSAM TomoSAM, a module of the PuMA software, has been developed as a plugin for 3D Slicer, a software platform used for 3D image processing and visualization. It utilizes the Segment Anything Model (SAM), a deep learning model capable of identifying objects and generating image masks based on minimal user input. This feature enables efficient segmentation of complex 3D datasets, particularly of woven materials, from tomography or similar imaging methods, reducing the need for manual segmentation.
Tomography↗
A Computational Study to Investigate the Effect of Defect Geometries on the Fatigue Crack Driving Forces in Powder-Bed AM Materials
Powder-bed additive manufacturing (AM) processes are associated with the formation of multiple types of process-specific pores, including but not limited to lack-of-fusion (LoF) and keyhole pores. The performance of an AM component is dependent on the type of pores, their density and their proximity to the free surface, and other heterogeneities in the microstructure. In order to characterize the influence of porosity on the mechanical behavior of AM materials, it is imperative to quantitatively analyze the heterogeneous strain accumulation in the vicinity of porosity. Process-specific microstructure models are generated using SPPARKS, an open-source process simulation code. Spherical keyhole or irregular LoF pores are embedded into the microstructure models, which are meshed and input into a finite element code, ScIFEN, to solve for the heterogeneous strain localization in the vicinity of the pores. Given the non-smooth geometries of LoF pores, they readily promote strain accumulation in their vicinity thereby increasing the propensity of initiating fatigue cracks.
Saikumar R Yeratapally↗
Vaporization heat transfer of dielectric liquids on enhanced surfaces covered with screen wicks
Experiments were conducted to investigate the vaporization heat transfer characteristics for the dielectric liquid FC-72 on several wicking surfaces which may be used in flat-plate heat pipes. The wicking materials studied included microstructure enhanced surfaces and coarse surfaces covered with screen meshes. Experimental data for q versus deltaT curves and critical heat fluxes were obtained for the two different operating conditions of a heat pipe, evaporation, and shallow pool boiling. When the liquid level was above the heated surface, the height of the liquid level above the surface was varied from 0 to 10 mm. When the liquid level was below the heated surface, the distance from the liquid level to the edge of the surface was adjusted from 0 to 15 mm. Experimental results revealed that for shallow pool boiling when the heated surface was covered with a wire screen mesh, the heat transfer coefficient increased at lower heat fluxes but the critical heat flux (CHF) decreased for all the surfaces tested. In the case of evaporation, both CHF and the heat transfer coefficient increased as the microstructure surfaces were covered with screen meshes.
Gu, C. B.↗
Multiscale Modeling of Ultra High Temperature Ceramics (UHTC) ZrB2 and HfB2: Application to Lattice Thermal Conductivity
We are developing a multiscale framework in computational modeling for the ultra high temperature ceramics (UHTC) ZrB2 and HfB2. These materials are characterized by high melting point, good strength, and reasonable oxidation resistance. They are candidate materials for a number of applications in extreme environments including sharp leading edges of hypersonic aircraft. In particular, we used a combination of ab initio methods, atomistic simulations and continuum computations to obtain insights into fundamental properties of these materials. Ab initio methods were used to compute basic structural, mechanical and thermal properties. From these results, a database was constructed to fit a Tersoff style interatomic potential suitable for atomistic simulations. These potentials were used to evaluate the lattice thermal conductivity of single crystals and the thermal resistance of simple grain boundaries. Finite element method (FEM) computations using atomistic results as inputs were performed with meshes constructed on SEM images thereby modeling the realistic microstructure. These continuum computations showed the reduction in thermal conductivity due to the grain boundary network.
Lawson, John W.↗
Multiscale Modeling of UHTC: Thermal Conductivity
We are developing a multiscale framework in computational modeling for the ultra high temperature ceramics (UHTC) ZrB2 and HfB2. These materials are characterized by high melting point, good strength, and reasonable oxidation resistance. They are candidate materials for a number of applications in extreme environments including sharp leading edges of hypersonic aircraft. In particular, we used a combination of ab initio methods, atomistic simulations and continuum computations to obtain insights into fundamental properties of these materials. Ab initio methods were used to compute basic structural, mechanical and thermal properties. From these results, a database was constructed to fit a Tersoff style interatomic potential suitable for atomistic simulations. These potentials were used to evaluate the lattice thermal conductivity of single crystals and the thermal resistance of simple grain boundaries. Finite element method (FEM) computations using atomistic results as inputs were performed with meshes constructed on SEM images thereby modeling the realistic microstructure. These continuum computations showed the reduction in thermal conductivity due to the grain boundary network.
Lawson, John W.↗
Physics-Based Modeling and Simulation of Self-Reacting Friction Stir Welding Using Computational Fluid Dynamics
A physics-based model was developed to simulate the behavior of material in a self-reacting friction stir welding (SR-FSW) process for the joining of metals. This steady-state model builds upon fundamental computational fluid dynamic (CFD) principles within Ansys Fluent to solve the discretized equations. The effective viscosity is calculated using a viscoplastic model using a Sheppard-Wright formulation of flow stress. Numerous advancements have been made in the incorporated physics including (1) temperature-dependent material properties; (2) locally adaptable flow and thermal boundary conditions; and (3) adapting material properties in nugget in response to microstructural changes. Simulation strategies to accelerate computation and improve numerical stability include adapting the mesh refinement and solver relaxation factors during simulation. The result is a highly robust and computationally efficient model capable of providing the material flow and temperature history across the domain. As material history determines the local microstructure and ultimately weld strength, an accurate and detailed physics-based model has the potential to accelerate SR-FSW process development. The model is highly adaptable to changes in process parameters, tool design, or alloy.
Process Modeling↗
Trabecular Bone Mechanical Properties and Fractal Dimension
Countermeasures for reducing bone loss and muscle atrophy due to extended exposure to the microgravity environment of space are continuing to be developed and improved. An important component of this effort is finite element modeling of the lower extremity and spinal column. These models will permit analysis and evaluation specific to each individual and thereby provide more efficient and effective exercise protocols. Inflight countermeasures and post-flight rehabilitation can then be customized and targeted on a case-by-case basis. Recent Summer Faculty Fellowship participants have focused upon finite element mesh generation, muscle force estimation, and fractal calculations of trabecular bone microstructure. Methods have been developed for generating the three-dimensional geometry of the femur from serial section magnetic resonance images (MRI). The use of MRI as an imaging modality avoids excessive exposure to radiation associated with X-ray based methods. These images can also detect trabecular bone microstructure and architecture. The goal of the current research is to determine the degree to which the fractal dimension of trabecular architecture can be used to predict the mechanical properties of trabecular bone tissue. The elastic modulus and the ultimate strength (or strain) can then be estimated from non-invasive, non-radiating imaging and incorporated into the finite element models to more accurately represent the bone tissue of each individual of interest. Trabecular bone specimens from the proximal tibia are being studied in this first phase of the work. Detailed protocols and procedures have been developed for carrying test specimens through all of the steps of a multi-faceted test program. The test program begins with MRI and X-ray imaging of the whole bones before excising a smaller workpiece from the proximal tibia region. High resolution MRI scans are then made and the piece further cut into slabs (roughly 1 cm thick). The slabs are X-rayed again and also scanned using dual-energy X-ray absorptiometry (DEXA). Cube specimens are then cut from the slabs and tested mechanically in compression. Correlations between mechanical properties and fractal dimension will then be examined to assess and quantify the predictive capability of the fractal calculations.
Hogan, Harry A.↗
Effects of Initial Powder Size on the Mechanical Properties and Microstructure of As-Extruded GRCop-84
GRCop-84 was developed to meet the mechanical and thermal property requirements for advanced regeneratively cooled rocket engine main combustion chamber liners. It is a ternary Cu- Cr-Nb alloy having approximately 8 at% Cr and 4 at% Nb. The chromium and niobium constituents combine to form 14 vol% Cr2Nb, the strengthening phase. The alloy is made by producing GRCop-84 powder through gas atomization and consolidating the powder using extrusion, hot isostatic pressing (HIP) or vacuum plasma spraying (VPS). GRCop-84 has been selected by Rocketdyne, Ratt & Wlutney and Aerojet for use in their next generation of rocket engines. GRCop-84 demonstrates favorable mechanical and thermal properties at elevated temperatures. Compared to NARloy-Z, the currently used inaterial in the Space Shuttle, GRCop-84 has approximately twice the yield strength, 10-1000 times the creep life, and 1.5-2.5 times the low cycle fatigue life. The thermal expansion of GRCop-84 is 7515% less than NARloy-Z which minimizes thermally induced stresses. The thermal conductivity of the two alloys is comparable at low temperature but NARloy-Z has a 20-50 W/mK thermal conductivity advantage at typical rocket engine hot wall temperatures. GRCop-84 is also much more microstructurally stable than NARloy-Z which translates into better long term stability of mechanical properties. Previous research into metal alloys fabricated by means of powder metallurgy (PM), has demonstrated that initial powder size can affect the microstructural development and mechanical properties of such materials. Grain size, strength, ductility, size of second phases, etc., have all been shown to vary with starting powder size in PM-alloys. This work focuses on characterizing the effect of varying starting powder size on the microstructural evolution and mechanical properties of as- extruded GRCop-84. Tensile tests and constant load creep tests were performed on extrusions of four powder meshes: +140 mesh (great3er than l05 micron powder size), -140 mesh (less than or equal to 105 microns), -140 plus or minus 270 (53 - 105 microns), and - 270 mesh (less than or equal to 53 microns). Samples were tested in tension at room temperature and at 500 C (932 F). Creep tests were performed under vacuum at 500 C using a stress of 111 MPa (16.1 ksi). The fracture surfaces of selected samples from both tests were studied using a Scanning Electron Microscope (SEM). The as-extruded materials were also studied, using both optical microscopy and SEM analysis, to characterize changes within the microstructure.
Okoro, Chika L.↗
Solution of free-boundary problems using finite-element/Newton methods and locally refined grids - Application to analysis of solidification microstructure
A new method is presented for the solution of free-boundary problems using Lagrangian finite element approximations defined on locally refined grids. The formulation allows for direct transition from coarse to fine grids without introducing non-conforming basis functions. The calculation of elemental stiffness matrices and residual vectors are unaffected by changes in the refinement level, which are accounted for in the loading of elemental data to the global stiffness matrix and residual vector. This technique for local mesh refinement is combined with recently developed mapping methods and Newton's method to form an efficient algorithm for the solution of free-boundary problems, as demonstrated here by sample calculations of cellular interfacial microstructure during directional solidification of a binary alloy.
Tsiveriotis, K.↗
Development of silicon nitride of improved toughness
The application of reaction sintered Si2N4 energy absorbing surface layers to hot-pressed Si3N4 was investigated. The surface layer was formed by in-place nitridation of silicon powder. It was found that reaction sintered Si3N4 layers of 1 mm thickness, fabricated from either -100, +200, -200, or -325 mesh Si powder and nitrided in 96% N2/4% H2 so that approximately 20-25 vol % unnitrided Si remained in the layer, resulted in a sevenfold increase in ballistic impact resistance of a 0.64 cm thick hot-pressed SI3N4 substrate from RT 1370 C. Both NC-132 SI3N4, with MgO additive, and NCX-34 Si3N4, with Y2O3 additive, were evaluated as substrate material. The finer grain size -200 and -325 mesh nitrided Si layers were for their smoothness and relatively high density. It was found that nitriding in N2/H2 mixtures, rather than pure N2, resulted in a microstructure that did not substantially degrade the strength of the hot-pressed Si3N4 substrate. Thermal cycling tests on the RSSN/HPSN combinations from 200 C to 1370 C for 75 cycles in air did not degrade the impact resistance nor the interfacial bonding, although a large amount of internal silica formation occurred within the RSSN layer. Mach 0.8, 5 hr, hot gas erosion tests showed no surface recession of RSSN layers at 1200 C and slight surface recession at 1370 C.
Brennan, J. J.↗
Finite Element Simulation of the Direct Energy Deposition using Comsol Multiphysics
Direct Energy Deposition (DED) is an emerging technology extensively employed in metal Additive Manufacturing (AM). Despite its widespread industrial application, mathematical modeling in this domain remains challenging. This complexity arises from the intricate nature of the modeling approach and the nonlinear behavior of material parameters across a broad temperature range. Consequently, experimentalists often resort to a trial-and-error method to achieve structures with desired properties. However, this approach can be time-consuming and may not always yield parts with the requisite characteristics, highlighting the necessity for mathematical modeling to enhance manufacturing success. This study focuses on thin-walled manufacturing with a single bead thickness, adjusting laser parameters to produce such structures. The laser cladding speed, typical for DED manufacturing, is considered to be on the order of centimeters per second. The various wall thicknesses and heights are explored to discern the general characteristics of walls manufactured via this DED approach. Our modeling approach diverges from the conventional DED modeling based on activation-deactivation of predefined mesh domains, commonly implemented in many finite element codes. Instead, a method is proposed that effectively models layer cladding and melt pool dynamics, enabling predictions of the microstructure in the resulting structures. The formation mechanisms of cellular, dendritic columnar, and stray (equiaxed) grains, which arise from the interplay between nucleation and growth from the surface is analyzed. The study also examines the feasibility of microstructure formation to demonstrate the various thermal characteristics inherent in wall manufacturing. Our results illustrate how different process parameters influence the temperature gradient and cooling rate of the molten pool, subsequently affecting the primary dendrite arm spacing (PDAS). This modeling technique allows for the investigation of diverse thermal conditions, facilitating the prediction of microstructure and residual stresses in the manufactured parts.
modeling↗
Test and Analysis of Composite Hat Stringer Pull-off Test Specimens
Hat stringer pull-off tests were performed to evaluate the delamination failure mechanisms in the flange region for a rod-reinforced hat stringer section. A special test fixture was used to pull the hat off the stringer while reacting the pull-off load through roller supports at both stringer flanges. Microscopic examinations of the failed specimens revealed that failure occurred at the ply termination in the flange area where the flange of the stiffener is built up by adding 45/-45 tape plies on the top surface. Test results indicated that the as-manufactured microstructure in the flange region has a strong influence on the delamination initiation and the associated pull-off loads. Finite element models were created for each specimen with a detailed mesh based on micrographs of the critical location. A fracture mechanics approach and a mixed mode delamination criterion were used to predict the onset of delamination and the pull-off load. By modeling the critical local details of each specimen from micrographs, the model was able to accurately predict the hat stringer pull-off loads and replicate the variability in the test results.
Li, Jian↗
Improved inhomogeneous finite elements for fabric reinforced composite mechanics analysis
There is a need to do routine stress/failure analysis of fabric reinforced composite microstructures to provide additional confidence in critical applications and guide materials development. Conventional methods of 3-D stress analysis are time consuming to set up, run and interpret. A need exists for simpler methods of modeling these structures and analyzing the models. The principal difficulty is the discrete element mesh generation problem. Inhomogeneous finite elements are worth investigating for application to these problems because they eliminate the mesh generation problem. However, there are penalties associated with these elements. Their convergence rates can be slow compared to homogeneous elements. Also, there is no accepted method for obtaining detailed stresses in the constituent materials of each element. This paper shows that the convergence rate can be significantly improved by a simple device which substitutes homogeneous elements for the inhomogeneous ones. The device is shown to work well in simple one and two dimensional problems. However, demonstration of the application to more complex two and three dimensional problems remains to be done. Work is also progressing toward more realistic fabric microstructural geometries.
Foye, R. L.↗
A Technique for Mapping Characteristic Lengths to Preserve Energy Dissipated via Strain Softening in a Multiscale Analysis
It is often advantageous to account for the microstructure of the material directly using multiscale modeling. For computational tractability, an idealized repeating unit cell (RUC) is used to capture all of the pertinent features of the microstructure. Typically, the RUC is dimensionless and depends only on the relative volume fractions of the different phases in the material. This works well for non-linear and inelastic behavior exhibiting a positive-definite constitutive response. Although, once the material exhibits strain softening, or localization, a mesh objective failure theories, such as smeared fracture theories, nodal and element enrichment theories (XFEM), cohesive elements or virtual crack closure technique (VCCT), can be utilized at the microscale, but the dimensions of the RUC must then be defined. One major challenge in multiscale progressive damage modeling is relating the characteristic lengths across the scales in order to preserve the energy that is dissipated via localization at the microscale. If there is no effort to relate the size of the macroscale element to the microscale RUC, then the energy that is dissipated will remain mesh dependent at the macroscale, even if it is regularized at the microscale. Here, a technique for mapping characteristic lengths across the scales is proposed. The RUC will be modeled using the generalized method of cells (GMC) micromechanics theory, and local failure in the matrix constituent subcells will be modeled using the crack band theory. The subcell characteristic lengths used in the crack band calculations will be mapped to the macroscale finite element in order to regularize the local energy in a manner consistent with the global length scale. Examples will be provided with and without the regularization, and they will be compared to a baseline case where the size and shape of the element and RUC are coincident (ensuring energy is preserved across the scales).
softening↗
Design optimization of space structures
The topology-shape-size optimization of space structures is investigated through Kikuchi's homogenization method. The method starts from a 'design domain block,' which is a region of space into which the structure is to materialize. This domain is initially filled with a finite element mesh, typically regular. Force and displacement boundary conditions corresponding to applied loads and supports are applied at specific points in the domain. An optimal structure is to be 'carved out' of the design under two conditions: (1) a cost function is to be minimized, and (2) equality or inequality constraints are to be satisfied. The 'carving' process is accomplished by letting microstructure holes develop and grow in elements during the optimization process. These holes have a rectangular shape in two dimensions and a cubical shape in three dimensions, and may also rotate with respect to the reference axes. The properties of the perforated element are obtained through an homogenization procedure. Once a hole reaches the volume of the element, that element effectively disappears. The project has two phases. In the first phase the method was implemented as the combination of two computer programs: a finite element module, and an optimization driver. In the second part, focus is on the application of this technique to planetary structures. The finite element part of the method was programmed for the two-dimensional case using four-node quadrilateral elements to cover the design domain. An element homogenization technique different from that of Kikuchi and coworkers was implemented. The optimization driver is based on an augmented Lagrangian optimizer, with the volume constraint treated as a Courant penalty function. The optimizer has to be especially tuned to this type of optimization because the number of design variables can reach into the thousands. The driver is presently under development.
Felippa, Carlos↗